Angular speeds and a basketball

In summary, the problem is asking for the fraction of total kinetic energy of a rolling basketball that is in the form of rotational kinetic energy. The answer is 2/5 and can be found by using the equations for translational and rotational kinetic energy, assuming the ball is rolling without slipping.
  • #1
anil
30
0
I don't know how to solve the following problem:

A basketball rolls along the floor with a constant linear speed V. (a) Find the fraction of its total kinetic energy that is in form of rotational kinetic energy about the center of ball.

I think the answer is 2/5. But i don't know how to do it.
 
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  • #2
The total KE is the sum of the translational and rotational KE (about center of mass).
The translational KE = 1/2 MV2
The rotational KE = 1/2 Iω2, where I is the rotational inertia of a spherical shell about its center (look it up!)

One can assume that it is rolling without slipping, which means that V = ωR.
 

FAQ: Angular speeds and a basketball

What is angular speed?

Angular speed is a measure of how fast an object is rotating or spinning around a fixed point. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

How is angular speed different from linear speed?

Linear speed refers to how fast an object is moving in a straight line, while angular speed refers to how fast an object is rotating around a fixed point. Angular speed is calculated by dividing the linear speed by the radius of the rotation.

How does angular speed affect a basketball?

The angular speed of a basketball affects how fast it rotates when it is in motion. A higher angular speed will cause the ball to spin faster, making it more difficult to catch or control.

What factors can affect the angular speed of a basketball?

The angular speed of a basketball can be affected by factors such as the force applied to the ball, the mass of the ball, and the air resistance it encounters while in motion.

Can the angular speed of a basketball change?

Yes, the angular speed of a basketball can change. It can increase or decrease depending on the external forces acting on the ball, such as a player's hand or the air resistance. The angular speed will also change if the ball changes its rotational axis or if there is a change in the radius of the rotation.

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